Measurement-based dynamic modeling of an electrical network

ABSTRACT

A system and a method for locally controlling delivery of electrical power along the distribution feeder by measuring certain electricity parameters of a distribution feeder line using a substation phasor measurement unit (PMU) electrically coupled to a substation distribution bus at a first node on the feeder line, and at least one customer site PMU electrically coupled to a low voltage end of a transformer at a customer site, wherein the transformer is coupled by a drop line to a second node on the distribution feeder line and the customer site is coupled by another drop line to the transformer, and by controlling at least one controllable reactive power resource and optionally a real power resource connected to the second node or at the customer site. Related apparatus, systems, articles, and techniques are also described.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.17/472,377, filed on Sep. 10, 2021, which is a continuation of U.S.application Ser. No. 16/600,356, filed on Oct. 11, 2019, which is acontinuation-in-part of and claims the benefit of international Appl.No. PCT/CA2018/050670, filed Jun. 5, 2018, which claims priority to U.S.Appl. No. 62/517,044 filed Jun. 8, 2017. U.S. application Ser. No.16/600,356 also claims priority to U.S. Appl. No. 62/744,873, filed onOct. 12, 2018, and claims priority to U.S. Appl. No. 62/744,874, filedon Oct. 12, 2018. The entire contents of each of the foregoing arehereby expressly incorporated by reference herein in their entireties.To the extent appropriate, a claim of priority is made to each of theabove disclosed applications.

FIELD

This disclosure relates generally to a system and method forcharacterizing and controlling aspects of an electrical distributionnetwork including feeder line parameters such as voltage, current, realpower, reactive power, and phase angle.

BACKGROUND

Management of an electrical utility distribution system has become achallenging and potentially costly problem. The widespread and growinginstallation of intermittent generation (e.g. solar, wind) connected tothis system is largely responsible for the challenges because this typeof generation was never included in the initial design of thedistribution system, and voltage variations caused by the intermittencyare lowering power quality of electricity delivered to customers coupledto distribution feeder lines of the system, and lowering the reliabilityof the system itself under some increasingly common circumstances.

SUMMARY

According to one aspect, there is provided a method for measuring one ormore electricity parameters of a distribution feeder line withoutdirectly connecting measurement sensors to it except at the substation,comprising: using a micro phasor measurement unit (μPMU) coupled to thedistribution feeder line at a first node at the substation, measuring avoltage phasor at the first node; using a μPMU at a customer's sitecoupled through the low voltage side of a voltage-reducing transformerat that customer site that has known, measurable, or calculatedproperties, wherein the transformer is coupled on its high voltage sideto the distribution feeder line at a second node by a drop line and toelectrical equipment at the customer's site on its low voltage side,including the customer site μPMU, by a drop line, where the μPMUmeasures a voltage phasor and a current phasor at the customer site withrespect to a specified time reference; determining the transformer anddrop line properties from measurements using environmental sensors andfrom configured parameters; determining a voltage drop impedance(voltage drop phasor) between the second node and the customer site μPMUfrom the transformer and drop line properties and a current phasormeasured by the customer site μPMU; determining a voltage phasor at thesecond node by adding the voltage phasor measured by the customer siteμPMU and the determined voltage drop impedance between the second nodeand the customer site μPMU; and determining the one or more electricityparameters of the distribution feeder line from the measured voltagephasor at the first node (substation) and the determined voltage phasorat the second node.

The electricity parameters include at least real power flow across afirst feeder line sector between the first node and second node,reactive power flow across the first feeder line sector, and current onthe first feeder line sector.

The voltage drop phasor between the second node and the customer sitecan be determined by the product of the measured current phasor at thecustomer site measurement unit and the drop impedance phasor between thesecond node and the customer site measurement unit, wherein the dropimpedance phasor is defined by:

$Z_{22\angle}\tan^{- 1}\frac{X_{22}}{R_{22}}$

wherein Z₂₂ represents the drop impedance between the second node andthe customer site measurement unit, X₂₂ represents the drop reactancebetween the second node and the customer site measurement unit, and R₂₂represents the drop resistance between the second node and the customersite measurement unit. X₂₂ and R₂₂ are known or calculated from thetransformer properties, the drop line properties, and sensormeasurements potentially taken at the location, such as outside airtemperature and transformer temperature. The additional measurements maybe used to increase the accuracy of the drop impedance calculation asnecessary depending on the application to which the electrical feederline parameters will be put.

The real power flow across a feeder line sector (a section of feederbetween two adjacent nodes) can be defined by:

$P_{ij} = {\frac{1}{R^{2} + X^{2}}\left( {{R{❘V_{i}❘}^{2}} - {R{❘V_{i}❘}{❘V_{j}❘}\cos\delta} + {X{❘V_{i}❘}{❘V_{j}❘}\sin\delta}} \right)}$

Wherein |V_(i)| is the magnitude of the voltage phasor at the upstreamnode (node i which is electrically closer to the substation), |V_(j)| isthe magnitude of the voltage phasor at the downstream node (node j whichis electrically further from the substation), δ is the angle of thevoltage phasor at the downstream node, and R and X are a resistance anda reactance of the first feeder line sector.

According to another aspect, there is provided a system for measuringone or more electricity parameters of a distribution feeder line,comprising: a μPMU located at a substation and coupled to a distributionfeeder line at a first node, for measuring a voltage phasor at the firstnode; at least one customer site μPMU coupled to a low voltage side of atransformer of at least one customer site, for measuring a voltagephasor and a current phasor at the customer site, and wherein thecustomer site μPMU is coupled to the distribution feeder line at asecond node through a drop line to a transformer that is coupled to thedistribution feeder line at the second node by a drop line; and aprocessor and a memory having encoded thereon program code executable bythe processor to:

-   -   (i) determine a voltage drop phasor between the second node and        the customer site measurement unit from a measured current        phasor and a measured voltage phasor at the customer site        measurement unit and a known, measured, or calculated drop        impedance between the second node and the customer site;    -   (ii) determine a voltage phasor at the second node by adding a        measured voltage phasor at the customer site measurement unit        and the determined voltage drop phasor between the second node        and the customer site; and    -   (iii) determine the one or more electricity parameters of the        distribution feeder line from a measured voltage phasor at the        first node and a determined voltage phasor at the second node.

According to another aspect, there is provided a method for locallycontrolling delivery of electrical power along a distribution feeder ofan electricity grid, wherein the distribution feeder comprises asubstation and a plurality of nodes, and the substation hastime-referenced voltage and current waveform measurement, and theplurality of nodes comprises connections carrying electrical energy to aplurality of customer sites through drop lines connected to voltagetransformers, and at least one customer site contains at least onecontrollable reactive power source and time-referenced voltage andcurrent waveform measurement wherein the time-reference at the customersite is the same or synchronized to the time reference at thesubstation. The method comprises: determining voltage and currentphasors at each of an upstream node and at a downstream node of thefeeder sector, where determining the phasors means computing the phasorsat the node from phasor measurements on lines connected to the nodethrough at least a transformer and a drop line; setting a target voltagephasor at the downstream node as a value that maintains the real powervalue at the upstream node, and when total reactive power injected atthe upstream and downstream nodes collectively generates all reactivepower consumed by the feeder sector, and adjusting operation of the atleast one controllable reactive power resource so that the actualvoltage magnitude at the downstream node moves towards the magnitude ofthe target voltage phasor. Adjusting the operation of the at least onecontrollable reactive power resource can comprise using a reactive powerdevice that increases reactive power to increase the actual voltagemagnitude and using a reactive power device that decreases reactivepower to decrease the actual voltage magnitude.

The plurality of customer sites can comprise at least one controllablereal power resource, in which case the method further comprises:adjusting operation of the at least one controllable real power resourceso that the actual phase angle at the downstream node moves towards thephase angle of the target voltage phasor.

The plurality of customer sites can include a node having anintermittent power generation source, in which case the method furthercomprises adjusting the target phasor setting at each node after achange in power generation from the intermittent power generationsource.

According to another aspect, there is provided a system for determiningvoltage and current phasors and locally controlling delivery ofelectrical power along a distribution feeder of an electricity grid. Thedistribution feeder comprises a substation and a plurality of nodes. Thesubstation has time-referenced voltage and current waveform measurement.The nodes comprise connections to customer sites for deliveringelectrical energy. The connections comprise drop lines and voltagetransformers. A pair of adjacent nodes define a feeder sector of thedistribution feeder wherein at least one of the nodes has a connectionto a customer site with at least one controllable reactive powerresource and time-referenced voltage and current waveform measurementwherein the time-reference at the customer site is the same orsynchronized to the time reference at the substation. The systemcomprises: at least two time-referenced voltage and current waveformmeasurement units with one of the measurement units at the substationand another at a customer site and the measurement units are have acommon time reference or are time synchronized with each other; at leastone reactive power resource controller communicative with and programmedto control operation of the at least one reactive power resource; and aserver computer communicative with the at least two time-referencedvoltage and current measurement units and with at least one reactivepower resource controller. The server computer comprises a processor anda memory having encoded thereon program code executable by the processorto:

-   -   (i) receive a voltage and current phasor measurements, or their        equivalents, from measurement units at a substation and at        customer sites coupled to a distribution feeder;    -   (ii) determine an actual voltage magnitude at an upstream node        and at a downstream node of the feeder sector, and a real power        value at the upstream node;    -   (iii) compute a target voltage phasor at the downstream node as        a value that improves the performance of the distribution feeder        or the equipment attached to it; and    -   (iv) transmit the target voltage phasor to the at least one        reactive power resource controller, such that the at least one        reactive power resource controller operates the at least one        controllable reactive power resource so that the actual voltage        magnitude at the downstream node moves towards the magnitude of        the target voltage phasor; and    -   (v) transmit a target voltage phase to any real power resource        controller, such that the real power resource controller        operates the at least on real power resource so that the actual        voltage phase at the downstream node moves toward the phase of        the target voltage phasor.

In one embodiment the target voltage phasor for a downstream node on afeeder sector is determined to maintain the real power value at theupstream node of the feeder sector, and when total reactive powerinjected at the upstream and downstream nodes collectively generates allreactive power consumed by the feeder sector.

Non-transitory computer program products (i.e., physically embodiedcomputer program products) are also described that store instructions,which when executed by one or more data processors of one or morecomputing systems, causes at least one data processor to performoperations herein. Similarly, computer systems are also described thatmay include one or more data processors and memory coupled to the one ormore data processors. The memory may temporarily or permanently storeinstructions that cause at least one processor to perform one or more ofthe operations described herein. In addition, methods can be implementedby one or more data processors either within a single computing systemor distributed among two or more computing systems. Such computingsystems can be connected and can exchange data and/or commands or otherinstructions or the like via one or more connections, including aconnection over a network (e.g. the Internet, a wireless wide areanetwork, a local area network, a wide area network, a wired network, orthe like), via a direct connection between one or more of the multiplecomputing systems, etc.

The details of one or more variations of the subject matter describedherein are set forth in the accompanying drawings and the descriptionbelow. Other features and advantages of the subject matter describedherein will be apparent from the description and drawings, and from theclaims.

DRAWINGS

FIG. 1 is a block diagram of an apparatus for providing distributedcontrol to resources on a distribution feeder of an electricity gridaccording to one embodiment.

FIG. 2 is a schematic diagram of the components of the system that allowdetermination of the voltage phasors at the nodes.

FIG. 3 is a schematic of a method and apparatus for measuring certainelectricity parameters on a distribution feeder line.

FIG. 4 is a schematic diagram of measuring electricity parameters on adistribution feeder line using the system shown in FIG. 2 .

FIG. 5 is a flow chart of steps performed in measuring electricityparameters on a distribution feeder.

FIG. 6 is a flowchart illustrating execution of a distributed powerdelivery control program on the central server computer to generatetarget phasor instructions for each controlled node on the distributionfeeder line according to a first embodiment.

FIG. 7 is a schematic illustration of a feeder sector and two adjacentnodes of the distribution feeder.

FIG. 8 is a flowchart illustrating execution of a distributed powerdelivery control program on the central server computer to generatetarget phasor instructions for each controlled node on the distributionfeeder line according to a second embodiment.

FIG. 9 is a flowchart illustrating execution of a distributed powerdelivery control program on the central server computer to generatetarget phasor instructions for each controlled node on the distributionfeeder line according to a third embodiment.

DETAILED DESCRIPTION

Distribution systems have been largely passive in nature, connectingutility substations to customer sites along a distribution feeder line.The utility has generally managed feeder lines (most typically voltagelevels on the lines) using measurements taken at the substation andusing controls also at the substation. For example, the utilitycompensates for low voltage at the end of the feeder by adjusting thesubstation voltage with a load tap changer (LTC), a purely mechanicaldevice on a transformer in the substation that is designed to correctslowly varying voltage and current changes by moving a physical contactthereby adjusting the turns ratio of the transformer. Additionally,capacitor banks installed along the distribution feeder line can providereactive power support to maintain customer site voltages within definedlimits. But these capacitor banks are usually only grossly controllableby at most a switch per capacitor bank. Intermittent generationconnected directly to the distribution system (as opposed to the bulktransmission system), especially from renewable sources, has brought avaluable source of energy to the electricity grid, but the intermittencyof generation and extremely coarse control have caused issues, largelybecause the designers of the distribution systems did not foresee theseuse cases. To address these issues, attempts have been made to measureand control certain parameters along distribution feeder lines.Referring to FIG. 3 , it is known to use a phasor measurement unit (PMU)200 to measure parameters of a distribution feeder line 201 byelectrically coupling the PMU 200 to a current transformer 202 (CT) anda potential transformer 203 (PT) that are respectively electricallycoupled to the feeder line 201. A PMU is a device which measures theelectrical waves on an electricity grid using a shared time source forsynchronization with one or more other PMUs. Time synchronization allowssynchronized, real-time measurements of multiple remote measurementspoints in an electricity grid. In particular, time synchronizationallows measurement of the relative angles between voltage waveforms andcurrent waveforms at different points on the distribution system. A PMUcan be a dedicated device, or PMU functionality can be incorporated intoa protective relay or other device.

However, measurements of feeder line parameters with PTs and CTs arecostly, typically involving two PTs and three CTs per installation,mounted at intervals along the distribution feeder line, and costing inthe order of $30,000-$50,000 per installation. Directly connecting PTsand CTs to the feeder lines requires large, expensive devices becausethe feeder lines typically operate at 10's of kilovolts (KV) and carryhundreds of amps (A) of current. This cost practically limits the numberof measurement points on the distribution feeder line that can bejustified. This scarcity of direct measurements of the voltage andcurrent waveforms has limited the control strategies that utilities havebeen able to use to manage distribution feeder voltage levels, energylosses, and substation equipment wear-and-tear. Historically this hasn'tbeen a big cost for utilities, but solar power and other intermittentpower generation on distribution feeders is driving up all of thesecosts.

In recent years, an increased penetration of intermittent generation inthe electricity grid is causing significant control problems. Forexample, connected solar capacity as low as 10% of peak capacity on adistribution feeder may result in voltage violations that are beyondANSI-defined limits. This intermittent generation capacity must bebalanced with either load or generation adjustments elsewhere on theelectricity grid in order to maintain system frequency. Often, ageneration facility used for balancing is located a significant distancefrom a feeder containing the intermittent generation resulting insignificant marginal power losses, which in some cases may exceed 30%.

Also, intermittent generation tends to cause voltage changes that canresult in poor customer power quality and excess wear-and-tear onsubstation tap changers. These substation tap changers incur increasedmaintenance needs and failure rates resulting from increased use causedby the intermittency. To avoid conflict between utility voltagemanagement systems that manage tap changes and voltage regulationcapability on solar inverters, as well as to avoid potential poorregulation caused by customer equipment, intermittent generatoroperators have been forbidden from regulating the system voltage (IEEE1547 and California Rule 21). Many electrical utilities have been usingtheir historical tools of monitoring line voltages at the substation andat a few points on the feeder and installing some in line capability toselectively manage voltage. This old-school approach tends to be slow inresponse time, and costly for the utility to implement.

Some utilities have made the investment in more comprehensivedistribution feeder measurement in order to use optimal power flowcontrol (OPF) algorithms. There are OPF algorithms generally known inthe art directed to minimizing loss or cost in an electricaldistribution system. There exists optimization algorithms andrelaxations which consider constraints such as generation limits,transmission thermal limits, bus voltage limits, number of switchingoperations etc. These algorithms tend to seek to solve the followingnon-linear power flow equations:

$\begin{matrix}{P_{k} = {V_{k}{\sum\limits_{n = 1}^{N}{Y_{kn}V_{n}\cos\left( {\delta_{k} - \delta_{n} - \theta_{kn}} \right)}}}} \\{Q_{k} = {V_{k}{\sum\limits_{n = 1}^{N}{Y_{kn}V_{n}\sin\left( {\delta_{k} - \delta_{n} - \theta_{kn}} \right)}}}}\end{matrix}$

where P_(k) and Q_(k) are real power (P) and reactive power (Q)delivered to bus k in a N bus system defined by Y_(kn) (Ybus matrix ofthe system) and V_(k), δ_(k) is the voltage magnitude and phase at bus kand θ_(kn) is the angle of the admittance Y_(kn).

Some OPF approaches lead to complex optimization problems requiring highcomputational resources, which can result in relatively slow reaction bypower control systems executing these algorithms.

As it is desirable to respond quickly to intermittent power generationin an electrical distribution system, it is desirable to provide a meansfor controlling power delivery in an electrical distribution system thatimproves on prior art approaches.

Embodiments of the subject matter described herein relate generally to asystem and a method for determining certain electricity parameters of adistribution feeder line using two or more micro phasor measurementunits (μPMU) electrically coupled to the feeder line, comprising asubstation μPMU electrically coupled to a substation distribution bus ata first node on the feeder line, and at least one customer site μPMUelectrically coupled to a low voltage side of a transformer at acustomer site. The transformer is coupled by a drop line to a secondnode on the distribution feeder line and the μPMU is coupled by a dropline to the transformer, and using the determined distribution feederline electricity parameters in a control system that computes targetvoltage phasors for each node on the feeder line which are then sent tovoltage management resource controllers collocated with the substationμPMU and customer site μPMU to control voltage management resources suchthat the actual voltage phasor at each node moves toward the targetvoltage phasor for the node.

A μPMU is a type of PMU that is a more appropriate for use on adistribution network because of its ability to measure small phases.PMU's used on transmission networks often measure phase to within 1degree which is adequate due to the high voltages and low currents ontransmission lines. These transmission line PMUs though must beconnected at 100's or even 1000's of kV, which is expensive and complex.Distribution lines operate at much lower voltages, and customer sites atlower voltages still. These μPMU's need to measure phase to within 0.01degrees because of the higher current but are easier to connect becauseof the lower voltages. Many μPMUs also include a GPS receiver to act asa time reference for all measurements.

In some implementations, the method comprises determining a voltage dropbetween the second μPMU and the second node on the distribution feederusing voltage and current phasor measurements taken by the second μPMUand knowing, measuring, and/or calculating the impedance (e.g., voltagedrop phasor) between the second node and the customer site μPMU giventhe transformer and the drop line properties and optionallyenvironmental measurements such as air temperature and transformertemperature. Then, the voltage phasor (voltage magnitude and phaseangle) at the second node can be calculated by adding the determinedvoltage drop and a customer site voltage phasor as measured by thesecond μPMU. Using the voltage phasors (the measured voltage phasor atthe substation, or the determined voltage phasor at any other node) fortwo adjacent nodes on the distribution feeder, electricity parameterssuch as real power, reactive power, and current across a feeder linesector between the adjacent nodes are determined. As a result, theelectricity parameters on the distribution feeder line can be measuredwithout the need to install relatively expensive PTs and CTs on thedistribution feeder line.

The method also comprises using the electricity parameters so determinedto compute loss in the distribution feeder sectors and compute targetvoltage phasors for each node that improve the performance of thedistribution line, where improved performance can include reduce energyloss, reduced mechanical wear-and-tear on substation components (such astap changes), and/or improved power quality delivered to customers. Thetarget voltage phasors can be used to control voltage managementresources electrically coupled to the nodes to cause the actual voltagephasor at each node to change in the direction of the target voltagephasor for that node and thereby improve the performance of thedistribution feeder.

In one embodiment the target voltage phasors are determined to meet afeeder line power loss threshold while reducing the mechanical movementof voltage management equipment at the substation, such as line tapchangers.

In another embodiment the target voltage phasors are determined to meetthe reactive power consumed by each feeder sector using Optimal PowerFlow calculations for a balanced, radial distribution system.

Throughout the disclosure where a server or computer is referenced itmay include one or more servers or computers in communication with eachother through one or more networks or communication mediums. Each serverand computer generally comprise one or more processors and one or morenon-transitory computer readable mediums in communication with eachother through one or more networks or communication mediums. The one ormore processors may comprise any suitable processing device known in theart, such as, for example, application specific circuits, programmablelogic controllers, field programmable gate arrays, microcontrollers,microprocessors, virtual machines, and electronic circuits. The one ormore computer readable mediums may comprise any suitable memory devicesknown in the art, such as, for example, random access memory, flashmemory, read only memory, hard disc drives, optical drives and opticaldrive media, or flash drives. In addition, where a network is referencedit may include one or more suitable networks known in the art, such as,for example, local area networks, wide area networks, intranets,extranets, virtual private networks, and the Internet. Further, where acommunication to a device or a direction of a device is referenced itmay be communicated over any suitable electronic communication mediumand in any suitable format known to in the art, such as, for example,wired or wireless mediums, compressed or uncompressed formats, encryptedor unencrypted formats.

System

According to one embodiment and referring to FIG. 1 , a local powercontrol system 10 for providing local control of power delivery along adistribution feeder 11 comprises a central server computer 12, μPMUs formeasuring voltage and current phasors on low voltage connections 20,controllers 13 for controlling real power resources 15, controllers 14for controlling reactive power resources 16 along the feeder(respectively referred to as “real power resource controllers” 13 and“reactive power resource controllers” 14), and controllers 18 forcontrolling utility voltage management devices 23. The controllers 13,14, 18 and the μPMUs 20 are communicative with the server computer 12over a network 19 such as the Internet, either directly or with theaddition of security tunnelling hardware or software; alternatively, theserver computer 12 can be fitted with dedicated communication links tothe controllers 13, 14, 18 and μPMUs 20 such as Frame Relay.

The distribution feeder 11 comprises a plurality of nodes 17 thatconnect to customer sites, wherein some customer sites have one or morecontrollable reactive power resources 16, some nodes 17 have one or morecontrollable real power resources 15 and other nodes 17 have one or morenon-controllable resources such as an intermittent power generationsource 22. For the sake of simplicity, FIG. 1 illustrates a first node17 having one controllable real power resource 15, a second node 17having two controllable reactive power resources 16, namely a reactivepower consuming device and a reactive power generating device, and athird node having a non-controllable solar power generation resource 22.The distribution feeder also comprises a substation comprising a μPMU 24coupled to the distribution line 11, one or more tap changers 23 alsocoupled to the distribution line 11, and/or other utility voltagemanagement devices.

The real and reactive power resources 15, 16 are typically located alongthe node sites 17 at locations remote from the server computer 12. Thereal power resources 15 can be electrical generators having capacity togenerate power (“generation resource”), electricity-powered deviceshaving capacity to consume a load (“load resource”), and storage deviceshaving capacity to store energy (“storage resource”) for short periodsand later release it back to the grid. Reactive power resources 16 that“generate” reactive power include capacitors, STATCOMs, solar (PV)inverters, and reactive power resources 16 that “consume” reactive powerinclude solar (PV) inverters and inductors.

In this example embodiment, the controllable real power resources 15 areall load resources, and in particular comprise multiple single-speedwater pumps, analog electrical boilers, and analog electrical blowers.These real power-consuming load resources 15 are normally intended toserve a primary process other than providing local power control to afeeder (herein referred to as “process load resources”), and the servercomputer 12 is configured to operate these load resources 15 to providelocal power control only within the operational constraints defined bythe original primary processes of these process load resources 15. Forexample, the water pumps are used primarily to regulate the water levelin a municipal water supply tank, each electrical boiler is usedprimarily to provide heat and domestic hot water for a building as partof a hybrid electric-gas heating system, and the blowers are usedprimarily to aerate a waste water treatment tank.

A load resource controller 13 that controls the process load resource 15and communicates with the remotely located server computer 12 isinstalled at the customer site which is connected to a node 17 through atransformer 21. A time-referenced μPMU 20 that communicates with theload resource controller 13 or the server computer 12 is also installedat the customer site and is coupled to the drop line that connects tothe low voltage side of the transformer 21. As will be explained indetail below, each load resource controller 13 receives target phasorsetpoints from the server computer 12 comprising a target voltagemagnitude and a target phase angle, and is programmed to operate theprocess load resource 15 at a load setpoint that causes the actual phaseangle at the node site 17 to move towards the target phase angle, but isalso programmed to only operate the process load resource 15 when theload setpoint is within the operational constraints of the process loadresource 15 (typically defined by the load resource's own controlsystem). In other words, the load resource controller 13 is programmedto allow the load resource's primary control system to override the loadresource controller 13 when the operators of the primary process requirethe process load resource 15 to be used for its primary processes. Forexample, a municipal water plant operator may require that a water tankbe kept between 10% and 90% full of water, and the load resourcecontroller 13 is programmed to allow the server computer 12 to operatethe pumps for this tank while the water level is within this range inorder to provide local power control to the feeder 11. However, when thewater level in the tank rises to 90% full, the load resource's controlsystem will be allowed to turn the pumps on, even if the server computer12 desires the pumps to be kept off. Controllable process load resources15 which are being used at a given time to serve their primary processare considered to be “off-line” to the server computer 12 and notavailable to provide local power control; conversely, controllable loadresources 15 which are within their primary operational constraints areconsidered “on-line” and available to be used to provide local powercontrol. “Off-line” load resources 15 are compensated for by the servercomputer 12 with other “on-line” load resources 15 so that the overallpower control functionality is preserved.

The load resource controller 13 in this embodiment is a small ruggedcomputer with capability to connect to the Internet 19, and to connectto the load resources 15 at their respective resource node sites 17. Theconnection between the load resource controller 13 and the servercomputer 12 is achieved through the internet 19, using a secure means ofcommunications. The load resource controller 13 is connected to thegeneration resource, load resource, or storage resource using one of anumber of methods, including: direct wiring to controllers or governorsof the load resource control system; direct connection to theSupervisory Control and Data Acquisition (SCADA) System used to controlthe process load resource 15 at the resource node site 17, or connectionto the network 19 used by the control system at the node site 17 thatcontrols the load resource 15. The real power resource controller 13 isalso connected to metering devices (not shown) that measure, tostandards required by an appropriate regulatory authority, the powerbeing delivered or consumed by the process load resources 15.

The load resource controller 13 may be connected to additionalmeasurement equipment (not shown) as required to ensure that operatingconstraints can be properly met, by: direct wiring to controllers ormeasurement equipment; direct connection to the SCADA System used tomeasure the process load resources 15 at the resource node site 17; orconnection to a network 19 used by the load resource's control system atthe node site 17 to measure the process load resource 15.

In operation, the load resource controller 13 will receive a targetphasor signal from the server computer 12, directing a change inconsumption or generation from one or more of the process load resources15 at the node site 17. The real power resource controller 13 willvalidate the received signal against the operating constraints of theprocess load resource 15 and clamp the signal if required. The controlsystem of the load resource 15 will send the setpoint signal to theprocess load resource 15 identified by the server computer 12,commanding the requested change.

At every update interval (e.g. 2 seconds), the μPMU will send voltageand current phasors or magnitudes and zero-crossing timestamps to theserver computer 12 directly or to the load resources controller 13 forlocal use or retransmission to the server computer 12, and the loadresources controller 13 will send a series of signals to the servercomputer 12, specifically:

-   -   The status or level of operation of each process load resource        15 at the resource node site 17 (there may be multiple load        resources connected to each load resource control system). The        load resource controller 13 will aggregate and send a total        power signal to the server computer 12, reflecting the power        generated or consumed at that site;    -   The load resource controller 13 will send a separate signal to        the server computer 12 to define the maximum and minimum power        levels that are available for the existing process load        resources 15 at the resource node site 17;    -   Any additional state information required by the server computer        12 to execute its costing subroutine, as will be described        below; and    -   An indicator if the load resource controller 13 itself, or the        SCADA, or the load resource control system, has suspended server        computer 12 control, and the current local control setpoint if        the server computer 12 control is suspended.

The load resource controller 13 will then store the command status andthe power levels measured for every resource at the resource node site17. Data storage at the local load resource controller 13 should besufficient to maintain all records for an extended period of time, forexample two years. The server computer 12 and the load resource 15 aretime-synchronized so that all time-stamped communications between nodes17 can be properly interpreted by the server computer 12 and the loadresource controller 13. The control and status protocol between theserver computer 12 and the load resource controller 13 insures thatnetwork issues (e.g. packet loss or reordering), does not causeincorrect control actions. The system will run continuously, with anintended cycle time between the server computer 12 and the load resourcecontroller 13 of about 5-10 seconds, and 5-60 seconds for largersystems. Local storage of data is maintained, time stamped in themeters, in the server computer 12 and in the control system of the loadresources 15.

Like the load resource controllers 13, the reactive power resourcecontrollers 14 are located at each node site 17 of reactive powerresources 16 along with a μPMU 20, and are operable to control theoperation of those reactive power resources 16. The reactive powerresource controller 14 has the same hardware design as the load resourcecontroller, and is programmed to control the reactive power resources16. Similarly, the utility resource controller 18 is of the same orsimilar hardware design as the load and reactive power resourcecontrollers 13, 14 with programming adapted to control the utilityvoltage management devices 23.

The server computer 12 is a redundant server computer system, equippedwith a reliable operating system such as Linux, real time software, anda long-term database. The server computer 12 is desirably installed at asecure location, protected from unauthorized physical access, wherethere is a reliable connection to the internet and a backed-up supply ofelectricity. For example, the server computer 12 may be installed at thesubstation. The server computer 12 may be a system that is spread acrossmultiple hardware chassis either to aggregate sufficient processingcapability, or to provide redundancy in the event of failure, or both.One chassis can operate as the primary server computer 12, and anotheras a backup server computer 12. Each chassis can run a multi-corecapable operating system. The server computer 12 runs a measurementprogram to process the measurements from the μPMUs and a control programto generate voltage target phasors for the resource controllers.

According to another example embodiment, the local power control system10 comprises controllers 14 for controlling reactive power resources butdoes not comprise controllers for controlling real power resources. Aswill be explained in more detail below, each reactive power resourcecontroller 14 receives target voltage phasor setpoints from the servercomputer 12, and is programmed to operate the reactive power resource 16at a setpoint that causes the actual voltage magnitude at the node 17 tomove towards the magnitude of the target voltage phasor setpoints. Sincethis alternative embodiment does not involve controlling real powerresources, the phase angle along the distribution line is notcontrolled. By controlling the reactive power, it is possible toinfluence the phase angle difference in a system that has an X/R ratioof line impedance of around 1.

According to an alternative embodiment the measurement program and thecontrol program are run on different computers.

Measurement Program

Referring to FIG. 2 , and according to one example embodiment, thefeeder line measurement part of the system, 100, comprises a programmedcomputer 102 and multiple μPMUs, namely a substation μPMU 104 coupled toa substation 110 on a distribution feeder line 108, and one or moreadditional μPMUs (“customer site μPMU”) which are each coupled to arespective transformer at a customer site, and wherein each transformeris coupled to the distribution feeder line 108 by a respective drop line109 and 111 and is coupled to the customer site by a respective dropline 116 and 117. In this embodiment, there are two customer site μPMUs,namely: a first μPMU 106 at a residential site 112 (“residential PMU”)coupled to a transformer 114 on a utility pole at that site(“residential transformer”), which in turn is coupled to the feeder line108 by a residential drop line 109; and, a second μPMU 107 at acommercial site 113 (“commercial μPMU”) coupled to a transformer 115 ina building on the commercial site 113 which in turn is coupled to thefeeder line 108 by a commercial drop line 111. While this embodimentshows two customer site μPMUs at two customer sites, the system 100 cancomprise as few as one customer site μPMU at one customer site, or morethan two customer site μPMUs at more than two customer sites.

The μPMUs 104, 106, 107 are devices that are capable of measuringelectricity parameters including voltage (V), current (I), real power(P) and reactive power (Q) in each phase. In addition to measuring theseelectricity parameters, the μPMUs 104, 106, 107 can measure thedifference in the voltage phase angle between two points on adistribution feeder line 108 by referencing a common or shared timereference or can measure the amplitude and zero-crossing timestamps ofvoltage and current waveforms. While μPMUs are used in this embodiment,other types of PMU as known in the art can be substituted.

Referring now to FIGS. 2 and 3 together, substation 110 is consideredthe start of the distribution feeder line 108 and is herein referred toas the “Node 1” of the distribution feeder line 108. The substation μPMU104 is installed in the substation 110, and thus provides the capabilityfor power, voltage and current measurements at Node 1, whereinmeasurements at Node 1 will be denoted by the subscript “1”. Theconnection point of residential drop line 109 to the distribution feederline 108 is herein referred to as “Node 2” of the distribution feederline 108 wherein measurements at Node 2 will be denoted by the subscript“2”, and the connection point of the commercial drop line 111 to thedistribution feeder line 108 is herein referred to as “Node 3” of thedistribution feeder line 108 wherein measurements at Node 3 will bedenoted by the subscript “3”. Although only three nodes are shown inFIGS. 2 and 3 for the sake of simplicity, the system 100 can comprisesadditional nodes with corresponding drop lines and customer sites.

The substation μPMU 104 will provide the reference angle for thedistribution feeder line 108. The phase angle of the voltage at thesubstation 110 is herein defined as δ₁=0. The current in the feeder line108 may have an angle ϕ₁₂, representing the power factor (PF) of afeeder line sector between the first and second nodes. The knownelectricity parameters at the substation (Node 1) are thus: voltagemagnitude |V₁|, voltage angle (which is 0 by definition, i.e. δ₁=0),current magnitude and phase angle (|I₁₂|, ϕ₁₂), and real and reactivepower leaving Node 1 (substation 110) for Node 2 (P₁₂ and Q₁₂).

The portion of the distribution feeder line 108 between Node 1 and Node2 is herein referred to as Feeder Sector 1, and the portion of thedistribution feeder line 108 between Node 2 and Node 3 is hereinreferred to Feeder Sector 2.

At Node 2, the electricity parameters are referenced as: voltage(|V₂|,δ₂), current along Feeder Sector 1 (|I₂₁|,ϕ₂₁), and real andreactive power leaving Node 2 for Node 1 (P₂₁ and Q₂₁). None of theseparameters are measured directly at Node 2, but can be determined frommeasurements taken by the substation and residential μPMUs 104, 106respectively as will be discussed in detail below. Similarly, theelectricity parameters at Node 3 are referenced as: voltage (|V₃|,δ₃),current along Feeder Sector 2 (|I₃₂|,ϕ₃₂), and real and reactive powerleaving Node 3 for Node 2 (P₃₂ and Q₃₂); none of these parameters aremeasured directly at Node 3, but can be determined from measurementstaken by the Node 1 substation 110 and commercial μPMUs 104, 107respectively in a similar manner as used to determine the parameters atNode 2.

At the residential site 112, power is delivered from the feeder line 108to a single customer that sees a distribution voltage drop ΔVacross theresidential drop line 109, the residential transformer 114, and dropline 116. The electricity parameter values at the residential site areherein denoted by the subscript “d2”. The residential μPMU 106 isconnected on the low voltage side of the residential transformer 114,and is configured to measure the consumption at the residential site112. This measurement may involve measurement of the voltage phasor(|V_(d2)|,δ_(d2)) and the current phasor (|_(d2)|,ϕ_(d2)) directly ifthe residential μPMU 106 has access to the timing reference measurementsof the substation μPMU 104 if the residential μPMU 106 is communicativewith substation μPMU 104. The measurement alternatively may involvemeasurement of the voltage magnitude and zero-crossing timestamps andthe current magnitude and current zero-crossing timestamps if theresidential μPMU 106 is not communicative directly with the substationμPMU 104. In this latter case, the calculation of the voltage phasor(|V_(d2)|,δ_(d2)) and the current phasor (|_(d2)|,ϕ_(d2)) at theresidential site 112 will be performed in the computer 102 which iscommunicative with both the residential μPMU 106 and the substation μPMU104. Of note, the voltage and current magnitudes are measured at theresidential site 112, and the voltage and current angles δ_(d2) andϕ_(d2) are measured or calculated against the reference of the voltagephasor at the substation μPMU 104. Consequently, the real power P_(d2),reactive power Q_(d2), voltage V_(d2) and current I_(d2) values from theresidential μPMU 106 readings measure the consumption at the residentialsite 112, and not the electricity parameter values in the distributionfeeder line 108. Similarly, the electricity parameter values at thecommercial site 113 are herein denoted by the subscript “d3”, and thecommercial μPMU 107 can measure the consumption at the commercial site113 to obtain and parameter values P_(d3), Q_(d3), |V_(d3)|, δ_(d3),|I_(d3)|, and ϕ_(d3).

The computer 102 in this embodiment is a computer server having aprocessor and a memory having encoded thereon a feeder line parametermeasurement program executable by the processor. The computer 102 iscommunicative with the substation μPMU 104 and with the customer siteμPMUs 106, 107 via a communications network in a manner known in theart. While in this embodiment the computer is shown at a location remotefrom and directly communicative with each of the substation μPMU 104 andcustomer site μPMUs 106, 107, the computer 102 and μPMUs 104, 106, 107can communicate in a different manner in the communication network aswould be known to one skilled in the art. For example, the computer 102can comprise multiple computer servers each directly coupled to acustomer site μPMU, and each customer site μPMU can be configured tocommunicate with the substation μPMU to receive measurement data fromthe substation μPMU, such that each computer server would receive thesubstation and customer site measurement data directly via itsconnection to the customer site μPMU. In another example, thefunctionality of computer 102 may be performed by one or more of theμPMUs. In another example, the μPMUs 104, 106, 107 may communicate withthe server computer 12 through gateways, such as local resourcecontrollers (FIGS. 1 13, 14, and 18).

The feeder line parameter measurement program when executed by thecomputer 102 can determine the phasor on the distribution feeder line108 at the connection points of each drop line. i.e. a second nodephasor (|V₂|,δ₂) at Node 2, and a third node phasor (|V₃|,δ₃) at Node 3.As described previously, it may determine intermediate values, such as(|V_(d2)|,δ_(d2)). (|I_(d2)|, ϕ_(d2)), (|V_(d3)|,δ_(d3)).(|I_(d3)|,ϕ_(d3)), first in order to calculate the second node phasorand third node phasor, as required. With the determined phasors at Node2 and Node 3, the feeder line parameter measurement program cancalculate the parameter values in a first sector of the feeder line 108connecting the substation 110 to the second node (Feeder Sector 1) andthe parameter values in a second sector of the feeder line 108connecting the second node to the third node (Feeder sector 2). For eachsubsequent node (not shown), the voltages and angles from the previousnode can be used to calculate the power flowing in the feeder line 108between the previous and current nodes.

The steps carried out by the feeder line parameter measurement programto calculate the feeder line parameters are now described with referenceto the diagram shown in FIG. 4 and the flowchart shown in FIG. 5 . Thefeeder line parameter measurement program uses measurement data taken bythe substation μPMU 104 and the customer site μPMUs 106, 107. For thesake of simplicity, the execution of the feeder line parametermeasurement program is described with reference to the measurementstaken by the residential μPMU 106 to determine the feeder line parametervalues, with the understanding that the steps to determine the feederline parameter values using the commercial μPMU 107 are similar.

The voltage and current phasors at the residential site(|V_(d2)|,δ_(d2)), (|I_(d2)|,ϕ_(d2)) are measured by the residentialμPMU 106 or calculated by the computer 102. The impedance between theresidential site 112 (i.e. at the location of the residential μPMU 106)and Node 2 is also used as an input by the feeder line parametermeasurement program, and can be represented as:

Z ₂₂ =R ₂₂ +jX ₂₂

wherein a resistance R₂₂ and a reactance X₂₂ (which includes theresistances and reactances of the drop lines 109, 116 and transformer114) are: known values from the properties of the drop lines 109, 116and transformer 114 at the residential site 112, measured by sensors atthe residential site 112, or calculated from known properties and sensormeasurements.

The voltage drop phasor (expressed as vector ΔV_(d2)) from the secondnode (Node 2) to the residential site 112 is calculated using (step401):

${{\Delta V}_{d2\angle}{\Delta\delta}_{d2}} = {\left( {I_{22\angle}\phi_{d2}} \right)\left( {Z_{22\angle}\tan^{- 1}\frac{X_{22}}{R_{22}}} \right)}$

wherein current magnitude 122 is the current along the residential dropline 109 and is assumed to be equal to the measured residential sitecurrent magnitude I_(d2), or calculated from the residential sitecurrent magnitude from a known or calculated current loss for theresidential transformer 114 (step 402).

The feeder line parameter measurement program then calculates thevoltage phasor at Node 2 (|V₂|,δ₂) by adding the measured residentialsite voltage and the calculated voltage drop between Node 2 and theresidential 112 site (Step 403), which is expressed mathematically as:

(|V ₂|,δ₂)=(|V _(d2)|,δ_(d2))+ΔV _(d2)<Δδ_(d2)

Once the voltage phasor at Node 1 is measured and the voltage phasor atNode 2 is determined, and the distribution feeder line impedance isknown, all other electricity parameter values along the distributionfeeder line 108 can be calculated by the feeder line parametermeasurement program. In particular, the real power flow P_(ij) (inWatts) and reactive power Q_(ij) (in VARs) flow between two nodes i, j,in the feeder line 108 are calculated by the feeder line parametermeasurement program (step 404 for Node 2 or 405 for Node 3 or greater)by applying the following general equations:

$P_{ij} = {\frac{1}{R^{2} + X^{2}}\left( {{R{❘V_{i}❘}^{2}} - {R{❘V_{i}❘}{❘V_{j}❘}\cos\delta} + {X{❘V_{i}❘}{❘V_{j}❘}\sin\delta}} \right){Watts}}$And$Q_{ij} = {\frac{1}{R^{2} + X^{2}}\left( {{X{❘V_{i}❘}^{2}} - {X{❘V_{i}❘}{❘V_{j}❘}\cos\delta} + {R{❘V_{i}❘}{❘V_{j}❘}\sin\delta}} \right){VARs}}$

wherein R and X are the resistance and reactance of the feeder linesector between nodes i and j, respectively and here i=1 and j=2.

The feeder line parameter measurement program then calculates theapparent power S_(ij) between Nodes i and j, in kilo volt-amps kVA (step406), by applying the following equations:

kVA _(ij) =S _(ij)=√{square root over (P _(ij) ² +Q _(ij) ²)}

And line currents are calculated by:

$I_{ij}^{*} = \frac{S_{ij}}{V_{ij}}$

wherein I_(ij)* is the complex conjugate of I_(ij).

The feeder line parameter measurement program then repeats thecalculations for each subsequent node, based on the voltages at thecurrent and subsequent nodes, and the angular difference between them.By executing this program, the system 100 provides a full set ofparameter values for the operation of the feeder line 108.

Where the feeder line is mixed with single phase loads, the method maybe applied to the single phase sectors of the feeder line.

While the illustrative embodiments of the present invention aredescribed in detail, it is not the intention of the applicant torestrict or in any way limit the scope of the appended claims to suchdetail. Additional advantages and modifications within the scope of theappended claims will readily be apparent to those skilled in the art.The invention in its broader aspects is therefore not limited to thespecific details, representative apparatus and methods, and illustrativeexamples shown and described. Accordingly, departures may be made fromsuch details without departing from the spirit or scope of the generalconcept.

Power Delivery Control Program

Referring to FIG. 1 , the server computer 12 has a processor and amemory on which is stored a power delivery control program which whenexecuted by the processor processes the distribution line electricalparameters and controls the utility voltage management devices 23 andthe real and reactive power resources 15, 16.

The power delivery control program controls the voltage along the feederline by controlling the operation of the reactive power resources 16 andthe utility voltage management devices 23 (collectively “voltagemanagement devices”) and controls the phase angle S along the feederline by controlling the operation of the real power resources 15.

Generally, the voltage magnitude between two adjacent nodes is similar,and the phase angle will generally be small. Under these conditions, thereal power flow in the feeder line will tend to track the phase angle δand the reactive power flow will track the difference in voltage betweenthe sending and receiving nodes. Using these principles and as will bedescribed in detail below, the power control program is able todetermine the target phasor (voltage magnitude and phase angle) at eachnode that is required to deliver power to the feeder line at a definedfeeder line power loss. The power control program also includes avoltage management device optimization module that can preferentiallyselect certain voltage management devices over others, by assigning anoperating cost to each voltage management device. In particular, thevoltage management device optimization module assigns a relatively highoperating cost to the substation tap changer 23 compared to the reactivepower resources 16 in order to minimize the use of the tap changer 23when controlling the voltage magnitude at each node along the feederline.

The power control program also includes a load resource managementmodule which comprises program code for determining which process loadresources are available to provide power control, and also to select acost-effective combination of available process load resources toprovide this control.

According to one embodiment, the power delivery control program controlsthe voltage management resources to deliver a required amount of powerto the feeder line 11 at an allowable voltage, while ensuring that thispower is delivered with a feeder line power loss that is below a definedthreshold and while minimizing the operation of the utility voltagemanagement devices 23 and in particular, the substation tap changer.

Referring now to FIG. 5 , the measurement program determines theelectrical parameters of the distribution line.

Referring now to FIG. 6 , the power control program when executeddetermines the target phasor of each node that is required to deliverpower to the feeder line under the desired conditions. e.g., withminimal substation tap changer operation and minimal feeder line powerloss, and selects the real and reactive power resources to meet thesedetermined target phasors. The total real and reactive power loss on thefeeder line 11 is calculated (step 500), by summing the real loss (i.e.I_(L) ²R_(L)) and reactive power loss (i.e. I_(L) ²X_(L)) on each linesector between the nodes.

The real and reactive power being removed or injected at each node 17 iscalculated using the measured actual phasor at the nodes 17 (step 502).The real and reactive power must sum to zero at each node 17, so powerin from an upstream location is equal to power removed at the node 17plus power flowing down the next line sector. The real and reactivepower at the sending (upstream) end of the line sector are determinedby:

$\begin{matrix}{{{Real}{Power}({Watts})} = {\frac{1}{R^{2} + X^{2}}\left( {{R{❘V_{S}❘}^{2}} - {R{❘V_{s}❘}{❘V_{R}❘}\cos\delta} + {X{❘V_{s}❘}{❘V_{R}❘}\sin\delta}} \right)}} & (1)\end{matrix}$ and, $\begin{matrix}{{{Reactive}{Power}({VARs})} = {\frac{1}{R^{2} + X_{2}}\left( {{X{❘V_{S}❘}^{2}} - {X{❘V_{s}❘}{❘V_{R}❘}\cos\delta} + {R{❘V_{s}❘}{❘V_{R}❘}\sin\delta}} \right)}} & (2)\end{matrix}$

wherein VS and VR are the sending and receiving end voltages of the linesector.

The real power and reactive power at the receiving (downstream) end ofthe line sector is:

$\begin{matrix}{{{Real}{Power}({Watts})} = {\frac{1}{R^{2} + X^{2}}\left( {{R{❘V_{R}❘}^{2}} - {R{❘V_{s}❘}{❘V_{R}❘}\cos\delta} + {X{❘V_{s}❘}{❘V_{R}❘}\sin\delta}} \right)}} & (3)\end{matrix}$ and $\begin{matrix}{{{Reactive}{Power}({VARs})} = {\frac{1}{R^{2} + X_{2}}\left( {{X{❘V_{R}❘}^{2}} - {X{❘V_{s}❘}{❘V_{R}❘}\cos\delta} + {R{❘V_{s}❘}{❘V_{R}❘}\sin\delta}} \right)}} & (4)\end{matrix}$

Of note, the real and reactive power going in at the sending end of theline sector is different than the power flowing out of the receiving endof the line sector because of real and reactive power loss in the linesector. In other words. Power In−Line Loss=Power Out for both real andreactive power on each line sector.

Next, the minimal power loss when delivering the required power to thefeeder line is calculated (step 502). To minimize power loss along thefeeder line 11, the power delivery should be controlled to minimizecurrent flow along the feeder line 11 while still meeting the powerdelivery and voltage requirements. This can be determined by selectingthe power flow leaving each node (sending node) so that the real powerleaving the sending node and going down the line sector is only enoughto provide for the load at the adjacent downstream node (receiving node)and the line loss along the line sector between the sending andreceiving nodes. Also, the reactive power on the line sector leavingeach node should be zero; in other words, a reactive power resource at anode should inject only enough reactive power to supply the reactivepower loss from the upstream line sector so that the outgoing linesector at the node carries no reactive power. Based on these principles,the allowable feeder line power loss threshold is calculated by:

-   -   a) starting at the end of the feeder line 11, calculate the        current I_(L), real power loss and reactive power loss on the        last line sector using the measurements of the load and actual        phasor at the last line sector;    -   b) calculate the real power delivered by the next upstream line        sector to be the real power required by nodes on the last line        sector plus the real power loss on that line sector, and    -   c) calculate the reactive power required from a reactive power        resource at the upstream node of the last line sector to be the        reactive power required to replace the reactive power used by        the last line sector.

Steps (a) to (c) are repeated at each upstream line sector for theentire feeder line 11 (i.e. back to the substation). The minimal totalfeeder line power loss is determined to be the sum of all of thedetermined line sector power losses.

Now that the reactive and real power at each node 17 to achieve theminimum total feeder line power loss have been determined, it ispossible to determine the voltage magnitude and phase angle settings ateach node 17 from equations (1) to (4). That is, equations (1) to (4)can be solved for |V_(S)|, |V_(R)| and δ for each line sector L of thefeeder line 11, working upwards from the last line sector and to thefirst line sector coupled to the substation.

An operational constraint is then assigned that represents the maximumallowable feeder line loss an operator will permit when controllingdelivery of power to the feeder line 11 (herein referred to as“allowable feeder line power loss threshold”). The allowable feeder linepower loss threshold can be set as the minimum feeder line power loss,in which case the determined voltage magnitudes and phase anglesrepresent the target phasor for each node that must be met in order toachieve the minimum total feeder line power loss (step 503).Alternatively, the allowable feeder line power loss threshold can be ahigher value as selected by an operator, in which case the targetvoltage magnitude and target phase angle are adjusted accordingly.

Next, the voltage management device optimization module is executed toselect the voltage management devices that will be used to meet thetarget voltage magnitude at each node (step 504). As noted previously,the voltage management devices include the controllable reactive powerresources 16 (i.e. capacitors, inductors, voltage inverters) at nodesites 17 and the utility voltage management devices 23 at thesubstation, and these devices 16, 23 can be used to control the reactivepower flows at each node 17 and the substation. As is well understood bythose skilled in the at, capacitive reactive power resources 16 increasereactive power and consequently increase voltage magnitude at a node 17and can be selected when the actual voltage magnitude is lower than thetarget voltage magnitude. Conversely, inductive reactive power resources16 consume reactive power and consequently decrease voltage magnitude ata node 17 and thus can be selected when the actual voltage magnitude ishigher than the target voltage magnitude.

The voltage management device optimization module determines whichvoltage management devices 16, 23 are available to achieve the targetvoltage magnitudes at each node 17, selects a cost effective combinationof available voltage management devices 16, 23, then sends controlsignals to controllers of those selected voltage management devices 16,23 to operate those devices accordingly. The selected combination can bethe combination that provides the lowest operating cost, or any one of anumber of combinations with have an operating cost below a selectedthreshold. Because not all nodes 17 may have a reactive power resource16 that can be controlled by the system 10, it may not be possible toachieve the target voltage magnitudes at each node 17, in which case,the power delivery control program selects the available reactive powerresources 16, 23 to come as close as possible to the target voltagemagnitude.

Because frequent use of the substation tap changer is generallyundesirable, the voltage management device optimization module assigns acomparatively higher operating cost to using the utility voltagemanagement devices 23 and a comparatively lower operating cost to usingthe capacitors, inductors, and invertors 16 at the customer sitesconnected to nodes 17. The cost function for each reactive device 16, 23is assigned based on actual cost. For example, a smart inverter canreact quickly with little cost, and as a result is assigned a relativelylow operating cost. Conversely, resources such as transformer tapchangers that have life limits based on operations, are assigned arelatively high operating cost. Once the operating cost is assigned toeach voltage management device 16, 23, a costing subroutine is executedto determine the available voltage management devices 16, 23 and theirrespective voltage settings.

Next, the power delivery control program executes a process loadresource management module to select the real power resources 15 thatwill be used to meet the target phase angle at each node 17 (step 505).As noted previously, the real power resources 15 include controllableprocess load resources 15 that serve a primary process, and can be usedby the system 10 to control phase angles along the feeder line 11provided that the usage does not exceed the operational constraintsdictated by the load resource's primary process. The use and selectionof such process load resources 15 to provide load is disclosed inco-owned PCT application publication no. WO 2011/085477, and is herebyincorporated by reference.

The process load resource management module includes program code whichdetermines which process load resources 14 are the most cost-effectiveto operate at any given time, then selects those process load resources15 to meet the target phasor angle at each node along the feeder line.In order to determine the relative cost to operate a process loadresource 15 at a particular point in time, the site control moduleprogramming includes a costing sub-routine which attributes a cost foroperating each process load resource 15 at a particular point in time.The costing subroutine takes into consideration factors such as the costthat must be paid to the primary process operator of the device 16 forusing the resource 16 at that time instance. The aggregated cost is thenmultiplied by a risk factor allocated to each resource 16 at that timeinstance; this risk factor takes into consideration the risk that overthe period of time the resource 16 will be used to provide powerdelivery control, the primary process operator will override feeder linepower control and use the resource 16 for its primary purpose. Thecosting sub-routine then selects a cost effective combination of processload resources to be operated; a cost effective combination can be thecombination of on-line load resources having the lowest operationalcost, or any one of a combination of load resources which fall within adefined operational cost budget.

Once the real power resources 15 and the reactive power resources 16 areselected, the system 10 transmits a control signal to the controller 13,14 at each real and reactive power resource 15, 16 that contains thetarget phasor for the node of the real and reactive power resource 15,16. The controllers 13, 14 then operate their associated real andreactive power resource 15, 16 to achieve the target phasor. That is,the load resource controller 13 will increase the load of its loadresource when the measured phase angle at the node is lower than thetarget phase angle and decrease the load when the measured phase angleis higher than the target phase angle. The reactive power resourcecontroller 14 will engage a capacitive resource 15 to generate reactivepower at a node 17 when the measured voltage magnitude at the node isbelow the target voltage magnitude, and will engage an inductiveresource 15 to consume reactive power at a node 17 when the measuredvoltage magnitude at the node 17 is below the target voltage magnitude.In this manner, the system 10 can provide localized control of thedelivery of power to each node 17 along the feeder line 11, at adesirably low feeder line power loss (assuming the allowable feeder linepower loss threshold is set at or near the minimum feeder line powerloss), while keeping the substation tap changer operation at a minimum(assuming the tap changer 23 is assigned a relatively high operationalcost).

Alternatively, the real power resources 15 can include generationresources, in which case, a process generation resource managementmodule is provided to select the generation resource that will be usedto meet the target phase angle at each node. Like the load resources,the generation resources can include resources which serve a primaryprocess, in which case the system only controls those generationresources that are on-line, i.e. within the operational constraints oftheir primary process. In a manner similar to selecting a cost-effectivecombination of load resources, a costing sub-routine is executed andeach available generation resource is assigned a relative operatingcost, and the most cost-effective combination of generation resources isselected to meet the target phasor angle at each node along the feederline. Once the generation resources are selected, the system 10 sends acontrol signal to each controller of the selected generation resourcethat contains the target phasor for the node of the generation resource.The controllers then operate their associated generation resource toachieve the target phasor. That is, the generation resource controllerwill increase the generation of its load resource when the measuredphase angle at the node is higher than the target phase angle, anddecrease the generation when the measured phase angle is lower than thetarget phase angle.

According to another embodiment, the power delivery control program usesoptimal power flow (OPF) algorithms that are based on a closed formsolution for radial distribution systems to control the utility voltagemanagement devices 23 and at least the reactive power resources 16 todeliver a required amount of reactive power to the feeder 11 to bringthe voltage to acceptable levels, while minimizing the power loss andminimizing the operation of the utility voltage management devices 23and in particular, the substation tap changer.

Such a closed form solution is expected to be more computationallytractable than complex generic algorithms which tend to be relativelycomputationally demanding; as a result, the power delivery controlprogram is expected to be able to react more quickly to changes in thedistribution feeder than a program executing complex optimizationproblems, which is desirable for distribution feeders containingintermittent generation sources such as solar and wind power generators.

An embodiment of the closed form solution used by the power deliverycontrol program to set the target phasor for each node will now bedescribed. This embodiment assumes a balanced, radial distributionsystem that can be reduced to a single-phase system. This embodiment isexpressed in polar form, and allows for a variable ratio of reactivepower injection at each of the upstream and downstream nodes i,j.

Referring to FIG. 7 , each feeder sector extends from an upstream node ito a downstream node j individually and assumes that the shuntcapacitance can be neglected. The voltage phasor at sending end V_(ij),the line current phasor I_(ij) and the line admittance Y_(ij) comprisingadmittance G_(ij)+j B_(ij), are defined as follows:

$\begin{matrix}{V_{i} = {{❘V_{i}❘}{\sphericalangle\delta}_{i}}} & (5)\end{matrix}$ $\begin{matrix}{V_{j} = {{❘V_{j}❘}{\sphericalangle\delta}_{j}}} & (6)\end{matrix}$ $\begin{matrix}{I_{ij} = {{❘I_{ij}❘}{\sphericalangle\delta}_{I_{ij}}}} & (7)\end{matrix}$ $\begin{matrix}{Y_{ij} = {{G_{ij} + {jB}_{ij}} = \frac{1}{R_{ij} + {jX}_{ij}}}} & (8)\end{matrix}$

wherein δ_(i) is the phase angle at node i. δ_(j) is the phase angle atnode j, and δ_(l) _(ij) the phase angle of the line current in the linesector ij.

The current (I_(ij)) in the feeder sector is defined as:

$I_{ij} = {{\left( {V_{i} - V_{j}} \right)Y_{ij}} = \frac{P_{ij} - {jQ}_{ij}}{V_{i}^{*}}}$

where V_(i) and V_(j) are the voltage phasors at sending and receivingend and Y_(ij) is the line admittance, P_(ij) is the real power flowfrom node i to node j and Q_(ij) is the reactive power flow from node ito node j.

P_(ij) in the feeder sector is expressed in equation (8) as:

P _(ij)=Re{((V _(i) −V _(j))(Y _(ij)))*V _(i)}  (10)

The power loss P_(loss ij) in the feeder sector is:

$\begin{matrix}{P_{{loss}{ij}} = {{R_{ij}{❘I_{ij}❘}^{2}} = {R_{ij}{❘\frac{P_{ij} - {jQ}_{ij}}{V_{i}^{*}}❘}^{2}}}} & (11)\end{matrix}$

The voltage drop from node i to node j ΔV_(ij) as defined in equation(10) is:

$\begin{matrix}{{\Delta V}_{ij} = {{V_{i} - V_{j}} = {\frac{{R_{ij}P_{ij}} + {X_{ij}Q_{ij}}}{V_{i}^{*}} + {j\frac{{X_{ij}P_{ij}} + {R_{ij}Q_{ij}}}{V_{i}^{*}}}}}} & (12)\end{matrix}$

If P_(ij)»Q_(ij) in (8) and (9), these equations reduce to equations(11) and (12):

$\begin{matrix}{P_{{loss}{ij}} = {R_{ij}{❘\frac{P_{ij}}{V_{i}^{*}}❘}^{2}}} & (13)\end{matrix}$ $\begin{matrix}{{\Delta V}_{ij} = {\frac{R_{ij}P_{ij}}{V_{i}^{*}} + {j\frac{X_{ij}P_{ij}}{V_{i}^{*}}}}} & (14)\end{matrix}$

Equations (13) and (14) suggest that reducing the reactance flow Q_(ij)from node i to node j significantly decreases the power loss P_(loss ij)and the voltage drop ΔV_(ij), for equal P_(ij). In the proposed closedform solution, the goal is to drive the voltage at the receiving endV_(j) to prevent reactive power flow Q_(ij) in the feeder sector whilemaintaining real power flow P_(ij) through the feeder sector. Theconsumed reactive power by the line (Q_(line)=|I_(ij)|² X_(ij)) will besupplied from the two adjacent nodes according to equation (13):

$\begin{matrix}{{aQ}_{ij} = {Q_{ji} = \frac{Q_{line}}{a + 1}}} & (15)\end{matrix}$

where a is the ratio between the reactive power supply from the sendingend Q_(ij) and receiving end Q_(ji) (“Q-ratio”). The two conditions leadto equations (27) where P_(ij) is the real power flow beforeoptimization that shall be maintained and therefore is a constantobtained by equation (8):

$\begin{matrix}\left\{ \begin{matrix}{{aQ}_{ij} = Q_{ji}} \\{P_{{ij}{new}} = P_{ij}}\end{matrix} \right. & (16)\end{matrix}$

Using the equation for complex power (S=VI*), equation (15) can beformulated:

$\begin{matrix}\left\{ \begin{matrix}{{{a \cdot {Im}}\left( {V_{i}I_{ij}^{*}} \right)} = {{Im}\left( {V_{j}\left( {- I_{ij}} \right)}^{*} \right)}} \\{{{Re}\left( {V_{i}I_{i}^{*}} \right)} = P_{ij}}\end{matrix} \right. & (17)\end{matrix}$

Substituting equations (3), (4) (5) in (14) and rearranging yieldsequation (16) with unknown |V_(j)|:

$\begin{matrix}{{\frac{\left( {P + {G_{ij}\left( {\frac{{\left( {{{Vi}^{2}a} - {Vj}^{2}} \right)B_{ij}^{2}} - {{G_{ij}\left( {P - {G_{ij}{Vi}^{2}}} \right)}\left( {a + 1} \right)}}{{\left( {a + 1} \right)B_{ij}^{2}} + {\left( {a + 1} \right)G_{ij}^{2}}} - {Vi}^{2}} \right)}} \right)^{2}}{B_{ij}^{2}} - \left( \frac{{\left( {{{Vi}^{2}a} - {Vj}^{2}} \right)B_{ij}^{2}} - {{G_{ij}\left( {P - {G_{ij}{Vi}^{2}}} \right)}\left( {a + 1} \right)}}{{\left( {a + 1} \right)B_{ij}^{2}} + {\left( {a + 1} \right)G_{ij}^{2}}} \right)^{2} - {{Vi}^{2}{Vj}^{2}}} = 0} & (18)\end{matrix}$

wherein each reference to “G”, “P”, “B” in equation (16) respectivelymeans “G_(ij)”, “P_(ij)” and “B_(ij)”

From equation (16), the voltage magnitude at the receiving end |V_(j)|,can be expressed as a function of the voltage magnitude at sending end|V₁|, the line admittance G_(ij), B_(ij) and power flow from node i tonode j P_(ij) and Q-ratio α to produce equation (17):

|V _(j) |=f(|V _(i) |,G _(ij) ,B _(ij) ,P _(ij) ,a)  (19)

Similarly, the voltage phase angle at receiving end δ_(i) can beexpressed as a function of the voltage magnitude at sending andreceiving end |V_(i)|, |V_(j)|, the line impedance G_(ij), B_(ij), andphase angle at sending end δ_(i) and Q-ratio α to produce equation (18):

δ_(j) =f(|V _(i) |,|V _(j) |,G _(ij) ,B _(ij),δ_(i) ,a)  (20)

Solving equation (18) leads to a closed form solution for |V_(j)| inequation (21) and δ_(j) in equation (22):

$\begin{matrix}{V_{i} = \sqrt{\frac{\begin{matrix}{{B_{ij}^{2}M} - {G_{ij}^{2}M} + {B_{ij}^{4}V_{i}^{2}} + {G_{ij}^{4}V_{i}^{2}} - {B_{ij}^{2}{aM}} - {G_{ij}^{2}{aM}} + {2G_{ij}^{4}V_{i}^{2}a} +} \\{{2B_{ij}^{2}G_{ij}^{2}V_{i}^{2}} + {B_{ij}^{4}V_{i}^{2}a^{2}} + {G_{ij}^{4}V_{i}^{2}a^{2}} - {4B_{ij}^{2}G_{ij}P_{ij}} + {2B_{ij}^{2}G_{ij}^{2}V_{i}^{2}a^{2}} +} \\{2B_{ij}^{2}G_{ij}^{2}V_{i}^{2}a}\end{matrix}}{{2B_{ij}^{4}} + {2B_{ij}^{2}G^{2}}}}} & (21)\end{matrix}$ where $M = \sqrt{\begin{matrix}\left( {{B_{ij}^{2}V_{i}^{2}} + {G_{ij}^{2}V_{i}^{2}} - {2B_{ij}P_{ij}} + {B_{ij}^{2}V_{i}^{2}a} + {G_{ij}^{2}V_{i}^{2}a}} \right) \\\left( {{B_{ij}^{2}V_{i}^{2}} + {G_{ij}^{2}V_{i}^{2}} + {2B_{ij}P_{ij}} + {B_{ij}^{2}V_{i}^{2}a} + {G_{ij}^{2}V_{i}^{2}a}} \right)\end{matrix}}$ $\begin{matrix}{\delta_{j} = {\delta_{j} - {\cos^{- 1}\left( \frac{{\left( {{aV}_{i}^{2} - V_{j}^{2}} \right)B_{ij}^{2}} - {{G_{ij}\left( {P - {G_{ij}V_{ij}^{2}}} \right)}\left( {a + 1} \right)}}{V_{i}{V_{j}\left( {{\left( {a - 1} \right)B_{ij}^{2}} + {\left( {a + 1} \right)G_{ij}^{2}}} \right)}} \right)}}} & (22)\end{matrix}$

Equations (21) and (22) provide a target voltage phasor at the receivingend of a feeder sector that assures that there is no Q flow while thereal power flow P_(ij) is maintained with respect to a given sending endvoltage phasor V_(i).

For a radial distribution system, the OPF solution provided in equations(21), (22) at each node can be calculated starting from the substation,successively node by node downstream to the feeder end. The advantage ofthe proposed closed-form OPF is its fast computation and that it doesnot require iterative power flow algorithms. Furthermore, it works forbi-directional power flow.

FIG. 8 is a flowchart illustrating a method for locally controllingdelivery of electrical power along a distribution feeder 11 using asystem 10 that executes the power delivery control program based on anembodiment wherein equal reactive power is injected at each node toconsume all the reactive power in the feeder sector. The system 10comprises controllers 13, 14 for controlling both controllable real andreactive power resources on the distribution feeder 11.

As noted above, the power delivery control program calculates the targetvoltage phasor for the downstream node 17 in each feeder sector of thefeeder distribution line 11 in succession, starting from the knownvoltage phasor at the substation 23 and working downstream one feedersector at a time (the phase angle at the substation is defined to be atangle zero). Thus, the first feeder sector in the distribution line 11uses the voltage phasor at the substation 23 as the input values for thereal and imaginary parts of the voltage at the upstream node v_(ire),v_(iim).

The power delivery control program is provided with or determines theadmittance value Y_(ij) of the feeder sector (step 700). The admittancecan be determined from the known resistance and reactance of the feedersector.

The real power at the upstream node i is available from the measurementprogram. As noted above, this value is input into the power deliverycontrol program as the power flow P_(ij) across the feeder sector (step701).

The inputted real and imaginary parts of the voltage at the upstreamnode v_(ire), v_(iim), the determined admittance value Y_(ij) and themeasured power flow value P_(ij) are used by the power delivery controlprogram in equations (14) and (15) to solve for the real and imaginaryparts of the voltage at the downstream node v_(jre), v_(jim). The targetvoltage phasor (comprising the target voltage magnitude and phase angle)at the downstream node is then determined by solving equations (16) and(17) (step 702).

The results of the measurement program also provide the actual phasor atthe downstream node 17. The actual phasor measurements consists of thevoltage magnitude |V| and angle δ at the downstream node 17. The realand/or reactive power controllers 13, 14 at the downstream node receivetheir target voltage phasor from the power delivery control program, andreceive the actual voltage phasor measurements from the measurementprogram. With these inputs, the real and/or reactive power controllers13, 14 can determine the difference between the actual voltage magnitudeand phase angle and the target voltage angle and phase angle.

The real and/or reactive power controllers 13, 14 then selects one ormore real and/or reactive power resources 15, 16 to control to cause theactual voltage magnitude and phase angle at the downstream node to movetowards its target voltage magnitude and phase angle, then operatestheir selected real and/or reactive power resources 15, 16 accordingly(step 703). As noted previously, the controllable reactive powerresources 16 at node sites 17 can be used to control the reactive powerinjection at each node 17 and the substation. As is well understood bythose skilled in the art, reactive power resources 16 such as capacitorsincrease reactive power and consequently increase voltage magnitude at anode 17 and can be selected when the actual voltage magnitude is lowerthan the target voltage magnitude. Conversely, reactive power resources16 that consume reactive power and consequently decrease voltagemagnitude at a node 17 can be selected when the actual voltage magnitudeis higher than the target voltage magnitude; examples of such reactivepower resources include PV inverters and static synchronous compensators(STATSCOMs), which can be operated in inductive mode to lower thevoltage as required.

The above steps are repeated for each line sector between two nodesalong the entire distribution feeder 11. For the first line sector, thereference voltage at the upstream node will be the voltage phasor at thesubstation 23. Applying steps 700 to 703 will provide a voltage targetat the downstream node (first node 17 after the substation 23). For thesecond line sector, the voltage phasor at the upstream node will be thetarget voltage phasor at the downstream node of the first line sector.This sequence is repeated for each feeder sector until the last node isreached within the distribution feeder 11.

FIG. 9 is a flowchart illustrating a method for locally controllingdelivery of electrical power along a distribution feeder 11 using asystem 10 that executes the power delivery control program based onanother embodiment of the closed-form solution, which is implemented inthe central control server 12 within a repeated routine. The centralcontrol server 12 obtains voltage phasors V_(i) and V_(j) at theupstream and downstream nodes using the results of the measurementprogram at each node i, j (step 800); determines the admittance of thefeeder Y_(ij) then calculates the actual power flow P_(ij) through eachfeeder sector using equation (23) (step 801); determines the lineadmittance values B_(ij) and G_(ij) then calculates the target voltagephasor of the downstream node j using the closed-form equations (21, 22)(step 802); ensures that target phasor is within the voltage limits of0.95 and 1.05 pu (steps 803-806); and dispatches target voltage phasorto the resource controller at the downstream node (step 807). Thisroutine is repeated continually for each successive pair of adjacentnodes.

In some embodiments, the real and/or reactive power resources 15, 16 donot have any operational constraints, and the power delivery controlprogram should be able to control the power delivery along the feedersector with a minimum power loss. In other embodiments, the real and/orreactive power resources can be provided with operational constraints.For example, an operational constraint can be assigned that representsthe maximum available reactive power resources. If the maximum availablereactive power resources are not sufficient to track the voltage phasortargets, a new set of target voltage phasors for the entire feeder lineshould be computed considering the reactive power constraints. Inanother example, an operational constraint can be assigned thatrepresents a maximum threshold on the line current in each sector, asthe feeders have a maximum current constraint.

There is provided, for managing an electrical grid distribution feederline responsively to characterized electrical parameters thereat, theline having a first line node being a substation with an associatedvoltage controller that is adapted to control the voltage thereat, and,downstream thereof, a second line node that is electrically coupled to acustomer's energy resource (that generates or consumes electricity), amethod of characterizing the voltage phasor at the second line node fora period of time, comprising the steps: (i) coupling a first μPMU atsaid first line node that is adapted to timestamp measure the electricalvoltage and current waveforms thereat; (ii) (a) coupling a voltagetransformer between said second line node and said customer's energyresource with drop lines, and (b) coupling a second μPMU on the dropbetween the transformer and said customer's energy resource, that isadapted to timestamp measure the electrical voltage and currentwaveforms thereat; (iii) making said first μPMU timestamped measurementsand making said second μPMU timestamped measurements andtime-synchronizing one of said first μPMU timestamped measurements withone of said second μPMU timestamped measurements; (iv) determining, forthe period, the impedances of said drop lines and said transformerbetween said second line node and said customer's energy resource; (v)determining, for the period, the voltage at the second line node basedon said drop line impedances and said transformer impedance and saidsecond μPMU measurements; and (vi) informing said determined second linenode voltage, to said voltage controller.

There is further provided the preceding wherein the customer's energyresource has a resource controller that is adapted to control the energyresource to change its real or reactive power consumption or generationto predictably cause a change in the voltage waveforms at the secondline node, and the voltage controller is adapted to determine voltagecontrol targets for the substation and the customer's energy resource,and additionally comprises the steps: (vii) determining a voltage targetfor the customer's energy resource coupled to the second line node; and(vii) determining a voltage target for the substation; and (viii)informing said determined voltage target at the second line node tocustomer's energy resource controller to adjust the voltage thereat.

There is further provided the preceding wherein the voltage target forthe substation control and the voltage target for the customer's energyresource control are determined to reduce the amount of substationcontrol needed.

There is further provided the preceding wherein the voltage target forthe substation control and the voltage target for the customer's energyresource control are determined to reduce the amount of energy lost inthe feeder line.

There is further provided the preceding wherein the voltage target forthe substation control and the voltage target for the customer's energyresource control are determined to trade off between the amount ofsubstation control and the amount of energy loss in the feeder line.

There is further provided the preceding wherein the trade off betweensubstation control and energy loss is based on the cost of wear and tearon the substation equipment and the value of the energy lost in thefeeder line.

There is further provided the preceding wherein the voltage target forthe substation control and the voltage target for the customer's energyresource control are determined to optimally minimize reactive powerflow in the feeder line subject to the constraints of the substationcontrol and the customer's energy resource and the costs of thewear-and-tear on the substation control and the impact to the customerof controlling its energy resource.

One or more aspects or features of the subject matter described hereincan be realized in digital electronic circuitry, integrated circuitry,specially designed application specific integrated circuits (ASICs),field programmable gate arrays (FPGAs) computer hardware, firmware,software, and/or combinations thereof. These various aspects or featurescan include implementation in one or more computer programs that areexecutable and/or interpretable on a programmable system including atleast one programmable processor, which can be special or generalpurpose, coupled to receive data and instructions from, and to transmitdata and instructions to, a storage system, at least one input device,and at least one output device. The programmable system or computingsystem may include clients and servers. A client and server aregenerally remote from each other and typically interact through acommunication network. The relationship of client and server arises byvirtue of computer programs running on the respective computers andhaving a client-server relationship to each other.

These computer programs, which can also be referred to as programs,software, software applications, applications, components, or code,include machine instructions for a programmable processor, and can beimplemented in a high-level procedural language, an object-orientedprogramming language, a functional programming language, a logicalprogramming language, and/or in assembly/machine language. As usedherein, the term “machine-readable medium” refers to any computerprogram product, apparatus and/or device, such as for example magneticdiscs, optical disks, memory, and Programmable Logic Devices (PLDs),used to provide machine instructions and/or data to a programmableprocessor, including a machine-readable medium that receives machineinstructions as a machine-readable signal. The term “machine-readablesignal” refers to any signal used to provide machine instructions and/ordata to a programmable processor. The machine-readable medium can storesuch machine instructions non-transitorily, such as for example as woulda non-transient solid-state memory or a magnetic hard drive or anyequivalent storage medium. The machine-readable medium can alternativelyor additionally store such machine instructions in a transient manner,such as for example as would a processor cache or other random accessmemory associated with one or more physical processor cores.

To provide for interaction with a user, one or more aspects or featuresof the subject matter described herein can be implemented on a computerhaving a display device, such as for example a cathode ray tube (CRT) ora liquid crystal display (LCD) or a light emitting diode (LED) monitorfor displaying information to the user and a keyboard and a pointingdevice, such as for example a mouse or a trackball, by which the usermay provide input to the computer. Other kinds of devices can be used toprovide for interaction with a user as well. For example, feedbackprovided to the user can be any form of sensory feedback, such as forexample visual feedback, auditory feedback, or tactile feedback; andinput from the user may be received in any form, including acoustic,speech, or tactile input. Other possible input devices include touchscreens or other touch-sensitive devices such as single or multi-pointresistive or capacitive trackpads, voice recognition hardware andsoftware, optical scanners, optical pointers, digital image capturedevices and associated interpretation software, and the like.

In the descriptions above and in the claims, phrases such as “at leastone of” or “one or more of” may occur followed by a conjunctive list ofelements or features. The term “and/or” may also occur in a list of twoor more elements or features. Unless otherwise implicitly or explicitlycontradicted by the context in which it is used, such a phrase isintended to mean any of the listed elements or features individually orany of the recited elements or features in combination with any of theother recited elements or features. For example, the phrases “at leastone of A and B;” “one or more of A and B;” and “A and/or B” are eachintended to mean “A alone, B alone, or A and B together.” A similarinterpretation is also intended for lists including three or more items.For example, the phrases “at least one of A, B, and C;” “one or more ofA, B, and C;” and “A. B, and/or C” are each intended to mean “A alone, Balone, C alone. A and B together. A and C together. B and C together, orA and B and C together.” In addition, use of the term “based on,” aboveand in the claims is intended to mean, “based at least in part on,” suchthat an unrecited feature or element is also permissible.

Although specific embodiments have been illustrated and describedherein, it should be appreciated that any arrangement which achieves thesame or similar purpose may be substituted for the embodiments describedor shown by the subject disclosure. The subject disclosure is intendedto cover any and all adaptations or variations of various embodiments.Combinations of the above embodiments, and other embodiments notspecifically described herein, can be used in the subject disclosure.For instance, one or more features from one or more embodiments can becombined with one or more features of one or more other embodiments. Inone or more embodiments, features that are positively recited can alsobe negatively recited and excluded from the embodiment with or withoutreplacement by another structural and/or functional feature. The stepsor functions described with respect to the embodiments of the subjectdisclosure can be performed in any order. The steps or functionsdescribed with respect to the embodiments of the subject disclosure canbe performed alone or in combination with other steps or functions ofthe subject disclosure, as well as from other embodiments or from othersteps that have not been described in the subject disclosure. Further,more than or less than all of the features described with respect to anembodiment can also be utilized.

1-21. (canceled)
 22. A method for controlling delivery of electric poweralong a distribution feeder line, the method comprising: receiving firstmeasurements from a first node on the distribution feeder line, whereinthe first measurements include measurements of electrical voltage andcurrent waveforms at the first node; receiving second measurements froma second node on the distribution feeder line, wherein the secondmeasurements include measurements of the electrical voltage and currentwaveform at the second node; determining, using the first measurementsand the second measurements, a target voltage phasor for the secondnode; and sending the target voltage phasor to the second node.
 23. Themethod of claim 22, wherein the first measurements and the secondmeasurements are timestamped measurements.
 24. The method of claim 23,further comprising time-synchronizing the timestamped measurements. 25.The method of claim 22, wherein: receiving the first measurementscomprises receiving the first measurements from a first micro phasormeasurement unit (μPMU) at the first node; and receiving the secondmeasurements comprises receiving the second measurements from a secondμPMU at the second node.
 26. The method of claim 22, wherein: sendingthe target voltage phasor to the second node comprises sending thetarget voltage phasor to a resource controller at the second node, theresource controller operable to control a resource using the targetvoltage phasor.
 27. The method of claim 22, wherein determining thetarget voltage phasor comprises: calculating a real power loss and areactive power loss of the distribution feeder line; determining a firstreal power flow and a first reactive power flow at the first node usingthe first measurements; determining a second real power flow and asecond reactive power flow at the second node using the secondmeasurements; determining a minimum distribution feeder line power lossusing the first real power flow, the first reactive power flow, thesecond real power flow, and the second reactive power flow; andcalculating the target voltage phasor for the second node based on theminimum distribution feeder line power loss.
 28. The method of claim 27,further comprising: determining electrical parameters of thedistribution feeder line, wherein calculating the real power loss andthe reactive power loss of the distribution feeder line comprises usingthe electrical parameters to calculate the real power loss and thereactive power loss.
 29. The method of claim 22, wherein: the first nodeis an upstream node and the second node is a downstream node; anddetermining the target voltage phasor comprises: determining anadmittance of the distribution feeder line between the first node andthe second node, calculating a real power at the first node using theadmittance, the first measurements, and the second measurements, andcalculating the target voltage phasor for the second node using theadmittance and the real power at the first node.
 30. The method of claim29, wherein determining the admittance comprises: determining aresistance and a reactance of the distribution feeder line; anddetermining the admittance using the resistance and the reactance. 31.The method of claim 30, wherein: determining the resistance and thereactance of the distribution feeder line comprises using any one of (a)transformer properties, (b) drop line properties, (c) sensormeasurements, or (d) any combination of (a)-(c) to determine theresistance and the reactance.
 32. The method of claim 22, wherein: thefirst node is an upstream node and the second node is a downstream node;and determining the target voltage phasor comprises: calculating a powerflow between the first node and the second node using the firstmeasurements and the second measurements, calculating the target voltagephasor for the second node using the power flow, the first measurements,and the second measurements, determining whether the target voltagephasor is withing a voltage limit, and when the target voltage phasor isnot withing the voltage limit, adjusting the target voltage phasor to bewithin the voltage limit.
 33. The method of claim 32, whereindetermining the target voltage phasor comprises: determining anadmittance of the distribution feeder line between the first node andthe second node, wherein calculating the power flow comprises using theadmittance to calculate the power flow.
 34. The method of claim 32,wherein the voltage limit has a lower limit of 0.95 pu and an upperlimit of 1.05 pu.
 35. A system controlling delivery of electric poweralong a distribution feeder line, the system comprising: a first microphasor measurement unit (μPMU) at a first node of the distributionfeeder line, wherein the first μPMU is operable to take firstmeasurements of the electrical voltage and current waveforms at thefirst node; a second μPMU at a second node of the distribution feederline, wherein the second μPMU is operable to take second measurements ofthe electrical voltage and current waveforms at the second node; aresource controller at the second node operable to control an energyresource at the second node; and a computer operable to: receive thefirst measurements from the first μPMU; receive the second measurementsfrom the second μPMU; determine a target voltage phasor for the secondnode using the first measurements and the second measurements; and sendthe target voltage phasor to the resource controller.
 36. The system ofclaim 35, wherein to determine the target voltage phasor comprises to:calculate a real power loss and a reactive power loss of thedistribution feeder line; determine a first real power flow and a firstreactive power flow at the first node using the first measurements;determine a second real power flow and a second reactive power flow atthe second node using the second measurements; determine a minimumdistribution feeder line power loss using the first real power flow, thefirst reactive power flow, the second real power flow, and the secondreactive power flow; and calculate the target voltage phasor for thesecond node based on the minimum distribution feeder line power loss.37. The system of claim 36, wherein the computer is further operable to:determine electrical parameters of the distribution feeder line, whereincalculating the real power loss and the reactive power loss of thedistribution feeder line comprises using the electrical parameters tocalculate the real power loss and the reactive power loss.
 38. Thesystem of claim 35, wherein to determine the target voltage phasorcomprises to: determine an admittance of the distribution feeder linebetween the first node and the second node; calculate a real power atthe first node using the admittance, the first measurements, and thesecond measurements; and calculate the target voltage phasor for thesecond node using the admittance and the real power at the first node.39. The system of claim 38, wherein to determine the admittancecomprises to: determine a resistance and a reactance of the distributionfeeder line; and determine the admittance using the resistance and thereactance.
 40. The system of claim 35, wherein to determine the targetvoltage phasor comprises to: calculate a power flow between the firstnode and the second node using the first measurements and the secondmeasurements; calculate the target voltage phasor for the second nodeusing the power flow, the first measurements, and the secondmeasurements; determine whether the target voltage phasor is withing avoltage limit; and when the target voltage phasor is not withing thevoltage limit, adjust the target voltage phasor to be within the voltagelimit.
 41. The system of claim 40, wherein the voltage limit has a lowerlimit of 0.95 pu and an upper limit of 1.05 pu.